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• How do I overload () operator with two parameters; like (3,5)?

  - by hkBattousai

  I have a mathematical matrix class. It contains a member function which is used to access any element of the class. template >class T> class Matrix { public: // ... void SetElement(T dbElement, uint64_t unRow, uint64_t unCol); // ... }; template <class T> void Matrix<T>::SetElement(T Element, uint64_t unRow, uint64_t unCol) { try { // "TheMatrix" is define as "std::vector<T> TheMatrix" TheMatrix.at(m_unColSize * unRow + unCol) = Element; } catch(std::out_of_range & e) { // Do error handling here } } I'm using this method in my code like this: // create a matrix with 2 rows and 3 columns whose elements are double Matrix<double> matrix(2, 3); // change the value of the element at 1st row and 2nd column to 6.78 matrix.SetElement(6.78, 1, 2); This works well, but I want to use operator overloading to simplify things, like below: Matrix<double> matrix(2, 3); matrix(1, 2) = 6.78; // HOW DO I DO THIS?

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• F# How to tokenise user input: separating numbers, units, words?

  - by David White

  I am fairly new to F#, but have spent the last few weeks reading reference materials. I wish to process a user-supplied input string, identifying and separating the constituent elements. For example, for this input: XYZ Hotel: 6 nights at 220EUR / night plus 17.5% tax the output should resemble something like a list of tuples: [ ("XYZ", Word); ("Hotel:", Word); ("6", Number); ("nights", Word); ("at", Operator); ("220", Number); ("EUR", CurrencyCode); ("/", Operator); ("night", Word); ("plus", Operator); ("17.5", Number); ("%", PerCent); ("tax", Word) ] Since I'm dealing with user input, it could be anything. Thus, expecting users to comply with a grammar is out of the question. I want to identify the numbers (could be integers, floats, negative...), the units of measure (optional, but could include SI or Imperial physical units, currency codes, counts such as "night/s" in my example), mathematical operators (as math symbols or as words including "at" "per", "of", "discount", etc), and all other words. I have the impression that I should use active pattern matching -- is that correct? -- but I'm not exactly sure how to start. Any pointers to appropriate reference material or similar examples would be great.

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• C++ template type deduction problem

  - by hamishmcn

  motivation: I would like to create a utility class so that instead of having to write: if( someVal == val1 || someVal == val2 || someVal == val3 ) I could instead write: if( is(someVal).in(val1, val2, val3) ) which is much closer to the mathematical 'a is an element of (b,c,d)' and also would save on a lot of typing when the variable name 'someVal' is long. Here is the code I have so far (for 2 and 3 values): template<class T> class is { private: T t_; public: is(T t) : t_(t) { } bool in(const T& v1, const T& v2) { return t_ == v1 || t_ == v2; } bool in(const T& v1, const T& v2, const T& v3) { return t_ == v1 || t_ == v2 || t_ == v3; } }; However it fails to compile if I write: is(1).in(3,4,5); instead I have to write is<int>(1).in(3,4,5); Which isn't too bad, but it would be better if somehow the compiler could figure out that the type is int with out me having to explicitly specify it. Is there anyway to do this or I am stuck with specifying it explicitly?

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• [C++] Trouble declaring and recognizing global functions

  - by Sarah

  I've created some mathematical functions that will be used in main() and by member functions in multiple host classes. I was thinking it would be easiest to make these math functions global in scope, but I'm not sure how to do this. I've currently put all the functions in a file called Rdraws.cpp, with the prototypes in Rdraws.h. Even with all the #includes and externs, I'm getting a "symbol not found" error at the first function call in main(). Here's what I have: // Rdraws.cpp #include <cstdlib> using namespace std; #include <cmath> #include "Rdraws.h" #include "rng.h" extern RNG rgen // this is the PRNG used in the simulation; global scope void rmultinom( double p_trans[], int numTrials, int numTrans, int numEachTrans[] ) { // function 1 def } void rmultinom( const double p_trans[], const int numTrials, int numTrans, int numEachTrans[]) { // function 2 def } int rbinom( int nTrials, double pLeaving ) { // function 3 def } // Rdraws.h #ifndef RDRAWS #define RDRAWS void rmultinom( double[], int, int, int[] ); void rmultinom( const double[], const int, int, int[] ); int rbinom( int, double ); #endif // main.cpp ... #include "Rdraws.h" ... extern void rmultinom(double p_trans[], int numTrials, int numTrans, int numEachTrans[]); extern void rmultinom(const double p_trans[], const int numTrials, int numTrans, int numEachTrans[]); extern int rbinom( int n, double p ); ... int main() { ... } I'm pretty new to programming. If there's a dramatically smarter way to do this, I'd love to know.

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• Operator overloading in generic struct: can I create overloads for specific kinds(?) of generic?

  - by Carson Myers

  I'm defining physical units in C#, using generic structs, and it was going okay until I got the error: One of the parameters of a binary operator must be the containing type when trying to overload the mathematical operators so that they convert between different units. So, I have something like this: public interface ScalarUnit { } public class Duration : ScalarUnit { } public struct Scalar<T> where T : ScalarUnit { public readonly double Value; public Scalar(double Value) { this.Value = Value; } public static implicit operator double(Scalar<T> Value) { return Value.Value; } } public interface VectorUnit { } public class Displacement : VectorUnit { } public class Velocity : VectorUnit { } public struct Vector<T> where T : VectorUnit { #... public static Vector<Velocity> operator /(Vector<Displacement> v1, Scalar<Duration> v2) { return new Vector<Velocity>(v1.Magnitude / v2, v1.Direction); } } There aren't any errors for the + and - operators, where I'm just working on a Vector<T>, but when I substitute a unit for T, suddenly it doesn't like it. Is there a way to make this work? I figured it would work, since Displacement implements the VectorUnit interface, and I have where T : VectorUnit in the struct header. Am I at least on the right track here? I'm new to C# so I have difficulty understanding what's going on sometimes.

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• Performance difference between functions and pattern matching in Mathematica

  - by Samsdram

  So Mathematica is different from other dialects of lisp because it blurs the lines between functions and macros. In Mathematica if a user wanted to write a mathematical function they would likely use pattern matching like f[x_]:= x*x instead of f=Function[{x},x*x] though both would return the same result when called with f[x]. My understanding is that the first approach is something equivalent to a lisp macro and in my experience is favored because of the more concise syntax. So I have two questions, is there a performance difference between executing functions versus the pattern matching/macro approach? Though part of me wouldn't be surprised if functions were actually transformed into some version of macros to allow features like Listable to be implemented. The reason I care about this question is because of the recent set of questions (1) (2) about trying to catch Mathematica errors in large programs. If most of the computations were defined in terms of Functions, it seems to me that keeping track of the order of evaluation and where the error originated would be easier than trying to catch the error after the input has been rewritten by the successive application of macros/patterns.

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• The best way to predict performance without actually porting the code?

  - by ardiyu07

  I believe there are people with the same experience with me, where he/she must give a (estimated) performance report of porting a program from sequential to parallel with some designated multicore hardwares, with a very few amount of time given. For instance, if a 10K LoC sequential program was given and executes on Intel i7-3770k (not vectorized) in 100 ms, how long would it take to run if one parallelizes the code to a Tesla C2075 with NVIDIA CUDA, given that all kinds of parallelizing optimization techniques were done? (but you're only given 2-4 days to report the performance? assume that you didn't know the algorithm at all. Or perhaps it'd be safer if we just assume that it's an impossible situation to finish the job) Therefore, I'm wondering, what most likely be the fastest way to give such performance report? Is it safe to calculate solely by the hardware's capability, such as GFLOPs peak and memory bandwidth rate? Is there a mathematical way to calculate it? If there is, please prove your method with the corresponding problem description and the algorithm, and also the target hardwares' specifications. Or perhaps there already exists such tool to (roughly) estimate code porting? (Please don't the answer: 'kill yourself is the fastest way.')

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• How can I integrate advanced computations into a database field?

  - by ciclistadan

  My biological research involves the measurement of a cellular structure as it changes length throughout the course of observation (capturing images every minute for several hours). As my data sets have become larger I am trying to store them in an Access database, from which I would like to perform various queries about their changes in size. I know that the SELECT statement can incorporate some mathematical permutations, but I have been unable to incorporate many of my necessary calculations (probably due to my lack of knowledge). For example, one calculation involves determining the rate of change during specifically defined periods of growth. This calculation is entirely dependent on the raw data saved in the table, therefore I didn't this it would be appropriate to just calculate it in excel prior to entry into the field. So my question is, what would be the most appropriate method of performing this calculation. Should I attempt to string together a huge SELECT calculation in my QUERY, or is there a way to use another language (I know perl?) which can be called to populate the new query field? I'm not looking for someone to write the code, just where is it appropriate to incorporate each step. Also, I am currently using Office Access but would be interested in any mySQL answers as I may be moving to this platform at a later date. Thanks all!

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• Separating code logic from the actual data structures. Best practices?

  - by Patrick

  I have an application that loads lots of data into memory (this is because it needs to perform some mathematical simulation on big data sets). This data comes from several database tables, that all refer to each other. The consistency rules on the data are rather complex, and looking up all the relevant data requires quite some hashes and other additional data structures on the data. Problem is that this data may also be changed interactively by the user in a dialog. When the user presses the OK button, I want to perform all the checks to see that he didn't introduce inconsistencies in the data. In practice all the data needs to be checked at once, so I cannot update my data set incrementally and perform the checks one by one. However, all the checking code work on the actual data set loaded in memory, and use the hashing and other data structures. This means I have to do the following: Take the user's changes from the dialog Apply them to the big data set Perform the checks on the big data set Undo all the changes if the checks fail I don't like this solution since other threads are also continuously using the data set, and I don't want to halt them while performing the checks. Also, the undo means that the old situation needs to be put aside, which is also not possible. An alternative is to separate the checking code from the data set (and let it work on explicitly given data, e.g. coming from the dialog) but this means that the checking code cannot use hashing and other additional data structures, because they only work on the big data set, making the checks much slower. What is a good practice to check user's changes on complex data before applying them to the 'application's' data set?

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• The most efficient way to calculate an integral in a dataset range

  - by Annalisa

  I have an array of 10 rows by 20 columns. Each columns corresponds to a data set that cannot be fitted with any sort of continuous mathematical function (it's a series of numbers derived experimentally). I would like to calculate the integral of each column between row 4 and row 8, then store the obtained result in a new array (20 rows x 1 column). I have tried using different scipy.integrate modules (e.g. quad, trpz,...). The problem is that, from what I understand, scipy.integrate must be applied to functions, and I am not sure how to convert each column of my initial array into a function. As an alternative, I thought of calculating the average of each column between row 4 and row 8, then multiply this number by 4 (i.e. 8-4=4, the x-interval) and then store this into my final 20x1 array. The problem is...ehm...that I don't know how to calculate the average over a given range. The question I am asking are: Which method is more efficient/straightforward? Can integrals be calculated over a data set like the one that I have described? How do I calculate the average over a range of rows?

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• Tools for Automated Source Code Editing

  - by Steve

  I'm working on a research project to automatically modify code to include advanced mathematical concepts (like adding random effects into a loop or encapsulating an existing function with a new function that adds in a more advanced physical model). My question to the community is: are there are any good tools for manipulating source code directly? I want to do things like Swap out functions Add variable declarations wherever they are required Determine if a function is multiplied by anything Determine what functions are called on a line of code See what parameters are passed to a function and replace them with alternatives Introduce new function calls on certain lines of code Wherever possible just leaving the rest of the code untouched and write out the results I never want to actually compile the code I only want to understand what symbols are used, replace and add in a syntactically correct way, and be able to declare variables at the right position. I've been using a minimal flex/bison approach with some success but I do not feel the it is robust. I hate to take on writing a full language parser just to add some new info to the end of a line or the top of a function. It seems like this is almost what is going to be required but it also seems like there should be some tools out there to do these types of manipulations already. The code to be changed is in a variety of languages, but I'm particularly interested in FORTRAN. Any thoughts?

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• Should I Teach My Son Programming? What approaches should I take? [closed]

  - by DaveDev

  I was wondering if it's a good idea to teach object oriented programming to my son? I was never really good at math as a kid, but I think since I've started programming it's given me a greater ability to understand math by being better able to visualise relationships between abstract models. I thought it might give him a better advantage in learning & applying logical & mathematical concepts throughout his life if he was able to take advantage of the tools available to programmers. what would be the best programming fields, techniques and/or concepts? What approach should I take? what concepts should I avoid? what fields of mathematics would he find this benfits him most? He's only 2 now so it wouldn't be for another few years before I do this, (and even at that, only from a very high level point of view). I thought I'd put it to the programming community and see what you guys thought? Possible Duplicate: What are some recommended programming resources for pre-teens?

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• Troubleshooting Network Speeds -- The Age Old Inquiry

  - by John K

  I'm looking for help with what I'm sure is an age old question. I've found myself in a situation of yearning to understand network throughput more clearly, but I can't seem to find information that makes it "click" We have a few servers distributed geographically, running various versions of Windows. Assuming we always use one host (a desktop) as the source, when copying data from that host to other servers across the country, we see a high variance in speed. In some cases, we can copy data at 12MB/s consistently, in others, we're seeing 0.8 MB/s. It should be noted, after testing 8 destinations, we always seem to be at either 0.6-0.8MB/s or 11-12 MB/s. In the building we're primarily concerned with, we have an OC-3 connection to our ISP. I know there are a lot of variables at play, but I guess I was hoping the experts here could help answer a few basic questions to help bolster my understanding. 1.) For older machines, running Windows XP, server 2003, etc, with a 100Mbps Ethernet card and 72 ms typical latency, does 0.8 MB/s sound at all reasonable? Or do you think that slow enough to indicate a problem? 2.) The classic "mathematical fastest speed" of "throughput = TCP window / latency," is, in our case, calculated to 0.8 MB/s (64Kb / 72 ms). My understanding is that is an upper bounds; that you would never expect to reach (due to overhead) let alone surpass that speed. In some cases though, we're seeing speeds of 12.3 MB/s. There are Steelhead accelerators scattered around the network, could those account for such a higher transfer rate? 3.) It's been suggested that the use SMB vs. SMB2 could explain the differences in speed. Indeed, as expected, packet captures show both being used depending on the OS versions in play, as we would expect. I understand what determines SMB2 being used or not, but I'm curious to know what kind of performance gain you can expect with SMB2. My problem simply seems to be a lack of experience, and more importantly, perspective, in terms of what are and are not reasonable network speeds. Could anyone help impart come context/perspective?

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• C# 4.0: Dynamic Programming

  - by Paulo Morgado

  The major feature of C# 4.0 is dynamic programming. Not just dynamic typing, but dynamic in broader sense, which means talking to anything that is not statically typed to be a .NET object. Dynamic Language Runtime The Dynamic Language Runtime (DLR) is piece of technology that unifies dynamic programming on the .NET platform, the same way the Common Language Runtime (CLR) has been a common platform for statically typed languages. The CLR always had dynamic capabilities. You could always use reflection, but its main goal was never to be a dynamic programming environment and there were some features missing. The DLR is built on top of the CLR and adds those missing features to the .NET platform. The Dynamic Language Runtime is the core infrastructure that consists of: Expression Trees The same expression trees used in LINQ, now improved to support statements. Dynamic Dispatch Dispatches invocations to the appropriate binder. Call Site Caching For improved efficiency. Dynamic languages and languages with dynamic capabilities are built on top of the DLR. IronPython and IronRuby were already built on top of the DLR, and now, the support for using the DLR is being added to C# and Visual Basic. Other languages built on top of the CLR are expected to also use the DLR in the future. Underneath the DLR there are binders that talk to a variety of different technologies: .NET Binder Allows to talk to .NET objects. JavaScript Binder Allows to talk to JavaScript in SilverLight. IronPython Binder Allows to talk to IronPython. IronRuby Binder Allows to talk to IronRuby. COM Binder Allows to talk to COM. Whit all these binders it is possible to have a single programming experience to talk to all these environments that are not statically typed .NET objects. The dynamic Static Type Let’s take this traditional statically typed code: Calculator calculator = GetCalculator(); int sum = calculator.Sum(10, 20); Because the variable that receives the return value of the GetCalulator method is statically typed to be of type Calculator and, because the Calculator type has an Add method that receives two integers and returns an integer, it is possible to call that Sum method and assign its return value to a variable statically typed as integer. Now lets suppose the calculator was not a statically typed .NET class, but, instead, a COM object or some .NET code we don’t know he type of. All of the sudden it gets very painful to call the Add method: object calculator = GetCalculator(); Type calculatorType = calculator.GetType(); object res = calculatorType.InvokeMember("Add", BindingFlags.InvokeMethod, null, calculator, new object[] { 10, 20 }); int sum = Convert.ToInt32(res); And what if the calculator was a JavaScript object? ScriptObject calculator = GetCalculator(); object res = calculator.Invoke("Add", 10, 20); int sum = Convert.ToInt32(res); For each dynamic domain we have a different programming experience and that makes it very hard to unify the code. With C# 4.0 it becomes possible to write code this way: dynamic calculator = GetCalculator(); int sum = calculator.Add(10, 20); You simply declare a variable who’s static type is dynamic. dynamic is a pseudo-keyword (like var) that indicates to the compiler that operations on the calculator object will be done dynamically. The way you should look at dynamic is that it’s just like object (System.Object) with dynamic semantics associated. Anything can be assigned to a dynamic. dynamic x = 1; dynamic y = "Hello"; dynamic z = new List<int> { 1, 2, 3 }; At run-time, all object will have a type. In the above example x is of type System.Int32. When one or more operands in an operation are typed dynamic, member selection is deferred to run-time instead of compile-time. Then the run-time type is substituted in all variables and normal overload resolution is done, just like it would happen at compile-time. The result of any dynamic operation is always dynamic and, when a dynamic object is assigned to something else, a dynamic conversion will occur. Code Resolution Method double x = 1.75; double y = Math.Abs(x); compile-time double Abs(double x) dynamic x = 1.75; dynamic y = Math.Abs(x); run-time double Abs(double x) dynamic x = 2; dynamic y = Math.Abs(x); run-time int Abs(int x) The above code will always be strongly typed. The difference is that, in the first case the method resolution is done at compile-time, and the others it’s done ate run-time. IDynamicMetaObjectObject The DLR is pre-wired to know .NET objects, COM objects and so forth but any dynamic language can implement their own objects or you can implement your own objects in C# through the implementation of the IDynamicMetaObjectProvider interface. When an object implements IDynamicMetaObjectProvider, it can participate in the resolution of how method calls and property access is done. The .NET Framework already provides two implementations of IDynamicMetaObjectProvider: DynamicObject : IDynamicMetaObjectProvider The DynamicObject class enables you to define which operations can be performed on dynamic objects and how to perform those operations. For example, you can define what happens when you try to get or set an object property, call a method, or perform standard mathematical operations such as addition and multiplication. ExpandoObject : IDynamicMetaObjectProvider The ExpandoObject class enables you to add and delete members of its instances at run time and also to set and get values of these members. This class supports dynamic binding, which enables you to use standard syntax like sampleObject.sampleMember, instead of more complex syntax like sampleObject.GetAttribute("sampleMember").

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• Formal Languages, Inductive Proofs &amp; Regular Expressions

  - by MarkPearl

  So I am slogging away at my UNISA stuff. I have just finished doing the initial once non stop read through the first 11 chapters of my COS 201 Textbook - “Introduction to Computer Theory 2nd Edition” by Daniel Cohen. It has been an interesting couple of days, with familiar concepts coming up as well as some new territory. In this posting I am going to cover the first couple of chapters of the book. Let start with Formal Languages… What exactly is a formal language? Pretty much a no duh question for me but still a good one to ask – a formal language is a language that is defined in a precise mathematical way. Does that mean that the English language is a formal language? I would say no – and my main motivation for this is that one can have an English sentence that is correct grammatically that is also ambiguous. For example the ambiguous sentence: "I once shot an elephant in my pyjamas.” For this and possibly many other reasons that I am unaware of, English is termed a “Natural Language”. So why the importance of formal languages in computer science? Again a no duh question in my mind… If we want computers to be effective and useful tools then we need them to be able to evaluate a series of commands in some form of language that when interpreted by the device no confusion will exist as to what we were requesting. Imagine the mayhem that would exist if a computer misinterpreted a command to print a document and instead decided to delete it. So what is a Formal Language made up of… For my study purposes a language is made up of a finite alphabet. For a formal language to exist there needs to be a specification on the language that will describe whether a string of characters has membership in the language or not. There are two basic ways to do this: By a “machine” that will recognize strings of the language (e.g. Finite Automata). By a rule that describes how strings of a language can be formed (e.g. Regular Expressions). When we use the phrase “string of characters”, we can also be referring to a “word”. What is an Inductive Proof? So I am not to far into my textbook and of course it starts referring to proofs and different types. I have had to go through several different approaches of proofs in the past, but I can never remember their formal names , so when I saw “inductive proof” I thought to myself – what the heck is that? Google to the rescue… An inductive proof is like a normal proof but it employs a neat trick which allows you to prove a statement about an arbitrary number n by first proving it is true when n is 1 and then assuming it is true for n=k and showing it is true for n=k+1. The idea is that if you want to show that someone can climb to the nth floor of a fire escape, you need only show that you can climb the ladder up to the fire escape (n=1) and then show that you know how to climb the stairs from any level of the fire escape (n=k) to the next level (n=k+1). Does this sound like a form of recursion? No surprise then that in the same chapter they deal with recursive definitions. An example of a recursive definition for the language EVEN would the 3 rules below: 2 is in EVEN If x is in EVEN then so is x+2 The only elements in the set EVEN are those that be produced by the rules above. Nothing to exciting… So if a definition for a language is done recursively, then it makes sense that the language can be proved using induction. Regular Expressions So I am wondering to myself what use is this all – in fact – I find this the biggest challenge to any university material is that it is quite hard to find the immediate practical applications of some theory in real life stuff. How great was my joy when I suddenly saw the word regular expression being introduced. I had been introduced to regular expressions on Stack Overflow where I was trying to recognize if some text measurement put in by a user was in a valid form or not. For instance, the imperial system of measurement where you have feet and inches can be represented in so many different ways. I had eventually turned to regular expressions as an easy way to check if my parser could correctly parse the text or not and convert it to a normalize measurement. So some rules about languages and regular expressions… Any finite language can be represented by at least one if not more regular expressions A regular expressions is almost a rule syntax for expressing how regular languages can be formed regular expressions are cool For a regular expression to be valid for a language it must be able to generate all the words in the language and no other words. This is important. It doesn’t help me if my regular expression parses 100% of my measurement texts but also lets one or two invalid texts to pass as well. Okay, so this posting jumps around a bit – but introduces some very basic fundamentals for the subject which will be built on in later postings… Time to go and do some practical examples now…

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• Agile Testing Days 2012 – Day 1 – The birth of the #unicorn…

  - by Chris George

  Still riding the high from the tutorial day, I arrived at the conference venue eager to get cracking with the days talks. The opening Keynote was “Disciplined Agile Delivery: The Foundation for Scaling Agile” presented by Scott Ambler. The general ideas behind the methodology such as not re-inventing the wheel, and being goal driven, not prescriptive in how you work certainly struck chords with how we are trying to work in my team. Scott made some interesting observations about how scrum is quite prescriptive and is this really agile? I agreed with quite a few of his points on how what works for one team may not work for another. How a team works should be driven by context and reflection, not process and prescription. However was somewhat dubious about some of the statistics he rolled out towards the end. However, out of this keynote was born something that was to transcend this one presentation. During the talk, Scott mentioned on more than one occasion “In the real world”, and at one point made reference to people living in the land of unicorns and rainbows. The challenge was then laid down on twitter for all speakers to include a unicorn in their presentations… and for the most part this happened! It became an identity for this years conference, and I’m sure something that any attendee will always associate with Agile Testing Days 2012! Following this keynote, I attended “Going agile with Automated GUI Testing – Some personal insights” by Jan Zdunek from codecentric on the vendor track. My speciality is test automation, and in particular GUI testing, so this drew me to this talk more than the others. Thankfully, it was made clear from the very start that this was not peddling any particular product (even though it was on the vendor track), and Jan faithfully stuck to that. Most of the content was not new to me, but it was really comforting to hear someone else with very similar experiences to my own. In particular, things like how GUI testing is hard and is not a silver bullet; how record & replay is NOT a good thing to do (which drew a somewhat inflammatory tweet from an automation company when I tweeted that!). Something that I have started hearing around the place, and has certainly been murmuring at work is to push more of the automation coding onto the developers. After all they are the coding experts. I agree with this to a degree, but I personally enjoy coding and find it very rewarding doing so, therefore I’d be reluctant to give it up. I think there are some better alternatives such as pairing with a developer. Lastly, Jan mentioned, almost in passing, that we should consider virtualisation for gui testing for covering configuration combinations. On my project we’ve been running our win32/.NET GUI tests in cloud virtualisation for a couple of years now… I really should write about that! After lunch the second keynote of the day was by Lisa Crispin and Janet Gregory,”Myths about Agile Testing, De-Bunked”. It started off well… with the two ladies donning Medusa style head bands whilst they disbanding several myths about agile testing! I got the impression that it was perhaps not as slick as they would have liked, but then Janet was suffering with a very sore throat so kept losing her voice. Nevertheless, the presentation was captivating, and they debunked several myths such as : “Testing is dead”, “Testers must write code”, “Agile teams always deliver faster”. I didn’t take many notes for this because it was being recorded, but unfortunately the recordings have not been posted yet so I’ll write more about this when they are. The TestLab was held during a somewhat free for all time during most of the afternoon. It looked intriguing and proved to be one of the surprising experiences of the conference for me. Run by James Lyndsay and Bart Knaack, it consisted of a number of ‘stations’ that offered different testing problems. I opted for testing a mathematical drawing app call Geogebra, the task being to pair up and exploratory test it. After an allotted time, we discussed issues we’d found and decided if we wanted to continue ‘playing’ to which we all agreed! It was fun! The last track talk of the day was “Developers Exploratory Testing – Raising the bar” by Sigge Birgisson. One of the teams at Red Gate have tried Dev or Team exploratory testing a couple of times, and I was really interested to go to the presentation that prompted that. I was not disappointed! Sigge gave a first class presentation, and not only explained what DET was all about, but also how to go about implementing it. Little tips like calling it a ‘workshop’ rather than ‘testing’ I can really see working! Monday evening saw the presentation of the award for the Most Influential Agile Testing Professional Person go to a much deserved Lisa Crispin. The evening was great, with acrobatics, magic and music. My Takeaway Triple from Day 1:  Some of the cool stuff that was suggested in the GUI Testing talk, we are already doing. I should write about that! Testing is not dead! Perhaps testing will become more of a skill than a specific role, but it is certainly not dead. Team/Developer exploratory testing… seems like a no-brainer assuming you have a team who is willing.  Day 2 – Coming soon…

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• Data Mining Resources

  - by Dejan Sarka

  There are many different types of analyses, each one with its own pros and cons. Relational reports have a predefined structure, and end users cannot change it. They are simple to use for end users. Reports can use real-time data and snapshots of data to show the state of a report at specific points in time. One of the drawbacks is that report authoring is limited to IT pros and advanced users. Any kind of dynamic restructuring is very limited. If real-time data is used for a report, the report has a negative impact on the performance of the source system. Processing of the reports might be slow because the data comes from relational database management systems, which are not optimized for reporting only. If you create a semantic model of your data, your end users can create ad-hoc report structures. However, the development is more complex because a developer is needed to create these semantic models. For OLAP, you typically use specialized database management systems. You get lightning speed of analyses. End users can use rich and thin clients to interactively change the structure of the report. Typically, they do it graphically. However, the development of an OLAP system is many times quite complex. It involves the preparation and maintenance of an enterprise data warehouse and OLAP cubes. In order to exploit the possibility of real-time restructuring of reports, the users must be both active and educated. The data is usually stale, as it is loaded into data warehouses and OLAP cubes with a scheduled process. With data mining, a structure is not selected in advance; it searches for the structure. As a result, data mining can give you the most valuable results because you can discover patterns you did not expect. A data mining model structure is limited only by the attributes that you use to train the model. One of the drawbacks is that a lot of knowledge is needed for a successful data mining project. End users have to understand the results. Subject matter experts and IT professionals need to understand business problem thoroughly. The development might be sometimes even more complex than the development of OLAP cubes. Each type of analysis has its own place in an enterprise system. SQL Server has tools for all kinds of analyses. However, data mining is the most advanced way of analyzing the data; this is the “I” in BI. In order to get the most out of it, you need to learn quite a lot. In this blog post, I am gathering together resources for learning, including forthcoming events. Books Multiple authors: SQL Server MVP Deep Dives – I wrote an introductory data mining chapter there. Erik Veerman, Teo Lachev and Dejan Sarka: MCTS Self-Paced Training Kit (Exam 70-448): Microsoft SQL Server 2008 - Business Intelligence Development and Maintenance – you can find a good overview of a complete BI solution, including data mining, in this book. Jamie MacLennan, ZhaoHui Tang, and Bogdan Crivat: Data Mining with Microsoft SQL Server 2008 – can’t miss this book if you want to mine your data with SQL Server tools. Michael Berry, Gordon Linoff: Mastering Data Mining: The Art and Science of Customer Relationship Management – data mining from both, business and technical perspective. Dorian Pyle: Data Preparation for Data Mining – an in-depth book about data preparation. Thomas and Ronald Wonnacott: Introductory Statistics – if you thought that you could get away without statistics, then you are not serious about data mining. Jiawei Han and Micheline Kamber: Data Mining Concepts and Techniques – in-depth explanation of the most popular data mining algorithms. Michael Berry and Gordon Linoff: Data Mining Techniques – another book that explains data mining algorithms, more fro a business perspective. Paolo Guidici: Applied Data Mining – very mathematical book, only if you enjoy statistics and mathematics in general. Forthcoming presentations I am presenting two data mining related sessions during the PASS Summit in Charlotte, NC: Wednesday, October 16th, 2013 - Fraud Detection: Notes from the Field – I am showing how to use data mining for a specific business problem. The presentation is based on real-life projects. Friday, October 18th: Excel 2013 Advanced Analytics – I am focusing on Excel Data Mining Add-ins, and how to use them together with Power Pivot and other add-ins. This is the most you can get out of Excel. Sinergija 2013, Belgrade, Serbia Tuesday, October 22nd: Excel 2013 Analytics to the Max – another presentation focusing on the most advanced analytics you can get in Excel. SQL Rally Amsterdam, Netherlands Thursday, November 7th: Advanced Analytics in Excel 2013 – and again I am presenting about data mining in Excel. Why three different titles for the same presentation? I don’t know, I guess I forgot the name I proposed every time right after I sent the proposal. Courses Data Mining with SQL Server 2012 – I wrote a 3-day course for SolidQ. If you are interested in this course, which I could also deliver in a shorter seminar way, you can contact your closes SolidQ subsidiary, or, of course, me directly on addresses [email protected] or [email protected]. This course could also complement the existing courseware portfolio of training providers, which are welcome to contact me as well. OK, now you know: no more excuses, start learning data mining, get the most out of your data

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• Towards an F# .NET Reflector add-in

  - by CliveT

  When I had the opportunity to spent some time during Red Gate's recent "down tools" week on a project of my choice, the obvious project was an F# add-in for Reflector . To be honest, this was a bit of a misnomer as the amount of time in the designated week for coding was really less than three days, so it was always unlikely that very much progress would be made in such a small amount of time (and that certainly proved to be the case), but I did learn some things from the experiment. Like lots of problems, one useful technique is to take examples, get them to work, and then generalise to get something that works across the board. Unfortunately, I didn't have enough time to do the last stage. The obvious first step is to take a few function definitions, starting with the obvious hello world, moving on to a non-recursive function and finishing with the ubiquitous recursive Fibonacci function. let rec printMessage message  =     printfn  message let foo x  =    (x + 1) let rec fib x  =     if (x >= 2) then (fib (x - 1) + fib (x - 2)) else 1 The major problem in decompiling these simple functions is that Reflector has an in-memory object model that is designed to support object-oriented languages. In particular it has a return statement that allows function bodies to finish early. I used some of the in-built functionality to take the IL and produce an in-memory object model for the language, but then needed to write a transformer to push the return statements to the top of the tree to make it easy to render the code into a functional language. This tree transform works in some scenarios, but not in others where we simply regenerate code that looks more like CPS style. The next thing to get working was library level bindings of values where these values are calculated at runtime. let x = [1 ; 2 ; 3 ; 4] let y = List.map  (fun x -> foo x) x The way that this is translated into a set of classes for the underlying platform means that the code needs to follow references around, from the property exposing the calculated value to the class in which the code for generating the value is embedded. One of the strongest selling points of functional languages is the algebraic datatypes, which allow definitions via standard mathematical-style inductive definitions across the union cases. type Foo =     | Something of int     | Nothing type 'a Foo2 =     | Something2 of 'a     | Nothing2 Such a definition is compiled into a number of classes for the cases of the union, which all inherit from a class representing the type itself. It wasn't too hard to get such a de-compilation happening in the cases I tried. What did I learn from this? Firstly, that there are various bits of functionality inside Reflector that it would be useful for us to allow add-in writers to access. In particular, there are various implementations of the Visitor pattern which implement algorithms such as calculating the number of references for particular variables, and which perform various substitutions which could be more generally useful to add-in writers. I hope to do something about this at some point in the future. Secondly, when you transform a functional language into something that runs on top of an object-based platform, you lose some fidelity in the representation. The F# compiler leaves attributes in place so that tools can tell which classes represent classes from the source program and which are there for purposes of the implementation, allowing the decompiler to regenerate these constructs again. However, decompilation technology is a long way from being able to take unannotated IL and transform it into a program in a different language. For a simple function definition, like Fibonacci, I could write a simple static function and have it come out in F# as the same function, but it would be practically impossible to take a mass of class definitions and have a decompiler translate it automatically into an F# algebraic data type. What have we got out of this? Some data on the feasibility of implementing an F# decompiler inside Reflector, though it's hard at the moment to say how long this would take to do. The work we did is included the 6.5 EAP for Reflector that you can get from the EAP forum. All things considered though, it was a useful way to gain more familiarity with the process of writing an add-in and understand difficulties other add-in authors might experience. If you'd like to check out a video of Down Tools Week, click here.

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• SQL SERVER – Number-Crunching with SQL Server – Exceed the Functionality of Excel

  - by Pinal Dave

  Imagine this. Your users have developed an Excel spreadsheet that extracts data from your SQL Server database, manipulates that data through the use of Excel formulas and, possibly, some VBA code which is then used to calculate P&L, hedging requirements or even risk numbers. Management comes to you and tells you that they need to get rid of the spreadsheet and that the results of the spreadsheet calculations need to be persisted on the database. SQL Server has a very small set of functions for analyzing data. Excel has hundreds of functions for analyzing data, with many of them focused on specific financial and statistical calculations. Is it even remotely possible that you can use SQL Server to replace the complex calculations being done in a spreadsheet? Westclintech has developed a library of functions that match or exceed the functionality of Excel’s functions and contains many functions that are not available in EXCEL. Their XLeratorDB library of functions contains over 700 functions that can be incorporated into T-SQL statements. XLeratorDB takes advantage of the SQL CLR architecture introduced in SQL Server 2005. SQL CLR permits managed code to be compiled into the database and run alongside built-in SQL Server functions like COUNT or SUM. The Westclintech developers have taken advantage of this architecture to bring robust analytical functions to the database. In our hypothetical spreadsheet, let’s assume that our users are using the YIELD function and that the data are extracted from a table in our database called BONDS. Here’s what the spreadsheet might look like. We go to column G and see that it contains the following formula. Obviously, SQL Server does not offer a native YIELD function. However, with XLeratorDB we can replicate this calculation in SQL Server with the following statement: SELECT *, wct.YIELD(CAST(GETDATE() AS date),Maturity,Rate,Price,100,Frequency,Basis) AS YIELD FROM BONDS This produces the following result. This illustrates one of the best features about XLeratorDB; it is so easy to use. Since I knew that the spreadsheet was using the YIELD function I could use the same function with the same calling structure to do the calculation in SQL Server. I didn’t need to know anything at all about the mechanics of calculating the yield on a bond. It was pretty close to cut and paste. In fact, that’s one way to construct the SQL. Just copy the function call from the cell in the spreadsheet and paste it into SMS and change the cell references to column names. I built the SQL for this query by starting with this. SELECT * ,YIELD(TODAY(),B2,C2,D2,100,E2,F2) FROM BONDS I then changed the cell references to column names. SELECT * --,YIELD(TODAY(),B2,C2,D2,100,E2,F2) ,YIELD(TODAY(),Maturity,Rate,Price,100,Frequency,Basis) FROM BONDS Finally, I replicated the TODAY() function using GETDATE() and added the schema name to the function name. SELECT * --,YIELD(TODAY(),B2,C2,D2,100,E2,F2) --,YIELD(TODAY(),Maturity,Rate,Price,100,Frequency,Basis) ,wct.YIELD(GETDATE(),Maturity,Rate,Price,100,Frequency,Basis) FROM BONDS Then I am able to execute the statement returning the results seen above. The XLeratorDB libraries are heavy on financial, statistical, and mathematical functions. Where there is an analog to an Excel function, the XLeratorDB function uses the same naming conventions and calling structure as the Excel function, but there are also hundreds of additional functions for SQL Server that are not found in Excel. You can find the functions by opening Object Explorer in SQL Server Management Studio (SSMS) and expanding the Programmability folder under the database where the functions have been installed. The  Functions folder expands to show 3 sub-folders: Table-valued Functions; Scalar-valued functions, Aggregate Functions, and System Functions. You can expand any of the first three folders to see the XLeratorDB functions. Since the wct.YIELD function is a scalar function, we will open the Scalar-valued Functions folder, scroll down to the wct.YIELD function and and click the plus sign (+) to display the input parameters. The functions are also Intellisense-enabled, with the input parameters displayed directly in the query tab. The Westclintech website contains documentation for all the functions including examples that can be copied directly into a query window and executed. There are also more one hundred articles on the site which go into more detail about how some of the functions work and demonstrate some of the extensive business processes that can be done in SQL Server using XLeratorDB functions and some T-SQL. XLeratorDB is organized into libraries: finance, statistics; math; strings; engineering; and financial options. There is also a windowing library for SQL Server 2005, 2008, and 2012 which provides functions for calculating things like running and moving averages (which were introduced in SQL Server 2012), FIFO inventory calculations, financial ratios and more, without having to use triangular joins. To get started you can download the XLeratorDB 15-day free trial from the Westclintech web site. It is a fully-functioning, unrestricted version of the software. If you need more than 15 days to evaluate the software, you can simply download another 15-day free trial. XLeratorDB is an easy and cost-effective way to start adding sophisticated data analysis to your SQL Server database without having to know anything more than T-SQL. Get XLeratorDB Today and Now! Reference: Pinal Dave (http://blog.sqlauthority.com)Filed under: PostADay, SQL, SQL Authority, SQL Query, SQL Server, SQL Tips and Tricks, T SQL Tagged: Excel

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• MCM Lab exam this week

  - by Rob Farley

  In two days I’ll’ve finished the MCM Lab exam, 88-971. If you do an internet search for 88-971, it’ll tell you the answer is –883. Obviously. It’ll also give you a link to the actual exam page, which is useful too, once you’ve finished being distracted by the calculator instead of going to the thing you’re actually looking for. (Do people actually search the internet for the results of mathematical questions? Really?) The list of Skills Measured for this exam is quite short, but can essentially be broken down into one word “Anything”. The Preparation Materials section is even better. Classroom Training – none available. Microsoft E-Learning – none available. Microsoft Press Books – none available. Practice Tests – none available. But there are links to Readiness Videos and a page which has no resources listed, but tells you a list of people who have already qualified. Three in Australia who have MCM SQL Server 2008 so far. The list doesn’t include some of the latest batch, such as Jason Strate or Tom LaRock. I’ve used SQL Server for almost 15 years. During that time I’ve been awarded SQL Server MVP seven times, but the MVP award doesn’t actually mean all that much when considering this particular certification. I know lots of MVPs who have tried this particular exam and failed – including Jason and Tom. Right now, I have no idea whether I’ll pass or not. People tell me I’ll pass no problem, but I honestly have no idea. There’s something about that “Anything” aspect that worries me. I keep looking at the list of things in the Readiness Videos, and think to myself “I’m comfortable with Resource Governor (or whatever) – that should be fine.” Except that then I feel like I maybe don’t know all the different things that can go wrong with Resource Governor (or whatever), and I wonder what kind of situations I’ll be faced with. And then I find myself looking through the stuff that’s explained in the videos, and wondering what kinds of things I should know that I don’t, and then I get amazingly bored and frustrated (after all, I tell people that these exams aren’t supposed to be studied for – you’ve been studying for the last 15 years, right?), and I figure “What’s the worst that can happen? A fail?” I’m told that the exam provides a list of scenarios (maybe 14 of them?) and you have 5.5 hours to complete them. When I say “complete”, I mean complete – you don’t get to leave them unfinished, that’ll get you ‘nil points’ for that scenario. Apparently no-one gets to complete all of them. Now, I’m a consultant. I get called on to fix the problems that people have on their SQL boxes. Sometimes this involves fixing corruption. Sometimes it’s figuring out some performance problem. Sometimes it’s as straight forward as getting past a full transaction log; sometimes it’s as tricky as recovering a database that has lost its metadata, without backups. Most situations aren’t a problem, but I also have the confidence of being able to do internet searches to verify my maths (in case I forget it’s –883). In the exam, I’ll have maybe twenty minutes per scenario (but if I need longer, I’ll have to take longer – no point in stopping half way if it takes more than twenty minutes, unless I don’t see an end coming up), so I’ll have time constraints too. And of course, I won’t have any of my usual tools. I can’t take scripts in, I can’t take staff members. Hopefully I can use the coffee machine that will be in the room. I figure it’s going to feel like one of those days when I’ve gone into a client site, and found that the problems are way worse than I expected, and that the site is down, with people standing over me needing me to get things right first time... ...so it should be fine, I’ve done that before. :) If I do fail, it won’t make me any less of a consultant. It won’t make me any less able to help all of my clients (including you if you get in touch – hehe), it’ll just mean that the particular problem might’ve taken me more than the twenty minutes that the exam gave me. @rob_farley PS: Apparently the done thing is to NOT advertise that you’re sitting the exam at a particular time, only that you’re expecting to take it at some point in the future. I think it’s akin to the idea of not telling people you’re pregnant for the first few months – it’s just in case the worst happens. Personally, I’m happy to tell you all that I’m going to take this exam the day after tomorrow (which is the 19th in the US, the 20th here). If I end up failing, you can all commiserate and tell me that I’m not actually as unqualified as I feel.

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• To Bit or Not To Bit

  - by Johnm

  'Twas a long day of troubleshooting and firefighting and now, with most of the office vacant, you face a blank scripting window to create a new table in his database. Many questions circle your mind like dirty water gurgling down the bathtub drain: "How normalized should this table be?", "Should I use an identity column?", "NVarchar or Varchar?", "Should this column be NULLABLE?", "I wonder what apple blue cheese bacon cheesecake tastes like?" Well, there are times when the mind goes it's own direction. A Bit About Bit At some point during your table creation efforts you will encounter the decision of whether to use the bit data type for a column. The bit data type is an integer data type that recognizes only the values of 1, 0 and NULL as valid. This data type is often utilized to store yes/no or true/false values. An example of its use would be a column called [IsGasoline] which would be intended to contain the value of 1 if the row's subject (a car) had a gasoline engine and a 0 if the subject did not have a gasoline engine. The bit data type can even be found in some of the system tables of SQL Server. For example, the sysssispackages table in the msdb database which contains SQL Server Integration Services Package information for the packages stored in SQL Server. This table contains a column called [IsEncrypted]. A value of 1 indicates that the package has been encrypted while the value of 0 indicates that it is not. I have learned that the most effective way to disperse the crowd that surrounds the office coffee machine is to engage into SQL Server debates. The bit data type has been one of the most reoccurring, as well as the most enjoyable, of these topics. It contains a practical side and a philosophical side. Practical Consideration This data type certainly has its place and is a valuable option for database design; but it is often used in situations where the answer is really not a pure true/false response. In addition, true/false values are not very informative or scalable. Let's use the previously noted [IsGasoline] column for illustration. While on the surface it appears to be a rather simple question when evaluating a car: "Does the car have a gasoline engine?" If the person entering data is entering a row for a Jeep Liberty, the response would be a 1 since it has a gasoline engine. If the person is entering data is entering a row for a Chevrolet Volt, the response would be a 0 since it is an electric engine. What happens when a person is entering a row for the gasoline/electric hybrid Toyota Prius? Would one person's conclusion be consistent with another person's conclusion? The argument could be made that the current intent for the database is to be used only for pure gasoline and pure electric engines; but this is where the scalability issue comes into play. With the use of a bit data type a database modification and data conversion would be required if the business decided to take on hybrid engines. Whereas, alternatively, if the int data type were used as a foreign key to a reference table containing the engine type options, the change to include the hybrid option would only require an entry into the reference table. Philosophical Consideration Since the bit data type is often used for true/false or yes/no data (also called Boolean) it presents a philosophical conundrum of what to do about the allowance of the NULL value. The inclusion of NULL in a true/false or yes/no response simply violates the logical principle of bivalence which states that "every proposition is either true or false". If NULL is not true, then it must be false. The mathematical laws of Boolean logic support this concept by stating that the only valid values of this scenario are 1 and 0. There is another way to look at this conundrum: NULL is also considered to be the absence of a response. In other words, it is the equivalent to "undecided". Anyone who watches the news can tell you that polls always include an "undecided" option. This could be considered a valid option in the world of yes/no/dunno. Through out all of these considerations I have discovered one absolute certainty: When you have found a person, or group of persons, who are willing to entertain a philosophical debate of the bit data type, you have found some true friends.

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• Is Data Science “Science”?

  - by BuckWoody

  I hold the term “science” in very high esteem. I grew up on the Space Coast in Florida, and eventually worked at the Kennedy Space Center, surrounded by very intelligent people who worked in various scientific fields. Recently a new term has entered the computing dialog – “Data Scientist”. Since it’s not a standard term, it has a lot of definitions, and in fact has been disputed as a correct term. After all, the reasoning goes, if there’s no such thing as “Data Science” then how can there be a Data Scientist? This argument has been made before, albeit with a different term – “Computer Science”. In Peter Denning’s excellent article “Is Computer Science Science” (April  2005/Vol. 48, No. 4 COMMUNICATIONS OF THE ACM) there are many points that separate “science” from “engineering” and even “art”.  I won’t repeat the content of that article here (I recommend you read it on your own) but will leverage the points he makes there. Definition of Science To ask the question “is data science ‘science’” then we need to start with a definition of terms. Various references put the definition into the same basic areas: Study of the physical world Systematic and/or disciplined study of a subject area ...and then they include the things studied, the bodies of knowledge and so on. The word itself comes from Latin, and means merely “to know” or “to study to know”. Greek divides knowledge further into “truth” (episteme), and practical use or effects (tekhne). Normally computing falls into the second realm. Definition of Data Science And now a more controversial definition: Data Science. This term is so new and perhaps so niche that the major dictionaries haven’t yet picked it up (my OED reference is older – can’t afford to pop for the online registration at present). Researching the term's general use I created an amalgam of the definitions this way: “Studying and applying mathematical and other techniques to derive information from complex data sets.” Using this definition, data science certainly seems to be science - it's learning about and studying some object or area using systematic methods. But implicit within the definition is the word “application”, which makes the process more akin to engineering or even technology than science. In fact, I find that using these techniques – and data itself – part of science, not science itself. I leave out the concept of studying data patterns or algorithms as part of this discipline. That is actually a domain I see within research, mathematics or computer science. That of course is a type of science, but does not seek for practical applications. As part of the argument against calling it “Data Science”, some point to the scientific method of creating a hypothesis, testing with controls, testing results against the hypothesis, and documenting for repeatability.  These are not steps that we often take in working with data. We normally start with a question, and fit patterns and algorithms to predict outcomes and find correlations. In this way Data Science is more akin to statistics (and in fact makes heavy use of them) in the process rather than starting with an assumption and following on with it. So, is Data Science “Science”? I’m uncertain – and I’m uncertain it matters. Even if we are facing rampant “title inflation” these days (does anyone introduce themselves as a secretary or supervisor anymore?) I can tolerate the term at least from the intent that we use data to study problems across a wide spectrum, rather than restricting it to a single domain. And I also understand those who have worked hard to achieve the very honorable title of “scientist” who have issues with those who borrow the term without asking. What do you think? Science, or not? Does it matter?

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• Why do we use Pythagoras in game physics?

  - by Starkers

  I've recently learned that we use Pythagoras a lot in our physics calculations and I'm afraid I don't really get the point. Here's an example from a book to make sure an object doesn't travel faster than a MAXIMUM_VELOCITY constant in the horizontal plane: MAXIMUM_VELOCITY = <any number>; SQUARED_MAXIMUM_VELOCITY = MAXIMUM_VELOCITY * MAXIMUM_VELOCITY; function animate(){ var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; x_velocity = x_velocity / scalar; z_velocity = x_velocity / scalar; } } Let's try this with some numbers: An object is attempting to move 5 units in x and 5 units in z. It should only be able to move 5 units horizontally in total! MAXIMUM_VELOCITY = 5; SQUARED_MAXIMUM_VELOCITY = 5 * 5; SQUARED_MAXIMUM_VELOCITY = 25; function animate(){ var x_velocity = 5; var z_velocity = 5; var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); var squared_horizontal_velocity = 5 * 5 + 5 * 5; var squared_horizontal_velocity = 25 + 25; var squared_horizontal_velocity = 50; // if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ if( 50 <= 25 ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; scalar = 50 / 25; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Now this works well, but we can do the same thing without Pythagoras: MAXIMUM_VELOCITY = 5; function animate(){ var x_velocity = 5; var z_velocity = 5; var horizontal_velocity = x_velocity + z_velocity; var horizontal_velocity = 5 + 5; var horizontal_velocity = 10; // if( horizontal_velocity >= MAXIMUM_VELOCITY ){ if( 10 >= 5 ){ scalar = horizontal_velocity / MAXIMUM_VELOCITY; scalar = 10 / 5; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Benefits of doing it without Pythagoras: Less lines Within those lines, it's easier to read what's going on ...and it takes less time to compute, as there are less multiplications Seems to me like computers and humans get a better deal without Pythagoras! However, I'm sure I'm wrong as I've seen Pythagoras' theorem in a number of reputable places, so I'd like someone to explain me the benefit of using Pythagoras to a maths newbie. Does this have anything to do with unit vectors? To me a unit vector is when we normalize a vector and turn it into a fraction. We do this by dividing the vector by a larger constant. I'm not sure what constant it is. The total size of the graph? Anyway, because it's a fraction, I take it, a unit vector is basically a graph that can fit inside a 3D grid with the x-axis running from -1 to 1, z-axis running from -1 to 1, and the y-axis running from -1 to 1. That's literally everything I know about unit vectors... not much :P And I fail to see their usefulness. Also, we're not really creating a unit vector in the above examples. Should I be determining the scalar like this: // a mathematical work-around of my own invention. There may be a cleverer way to do this! I've also made up my own terms such as 'divisive_scalar' so don't bother googling var divisive_scalar = (squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY); var divisive_scalar = ( 50 / 25 ); var divisive_scalar = 2; var multiplicative_scalar = (divisive_scalar / (2*divisive_scalar)); var multiplicative_scalar = (2 / (2*2)); var multiplicative_scalar = (2 / 4); var multiplicative_scalar = 0.5; x_velocity = x_velocity * multiplicative_scalar x_velocity = 5 * 0.5 x_velocity = 2.5 Again, I can't see why this is better, but it's more "unit-vector-y" because the multiplicative_scalar is a unit_vector? As you can see, I use words such as "unit-vector-y" so I'm really not a maths whiz! Also aware that unit vectors might have nothing to do with Pythagoras so ignore all of this if I'm barking up the wrong tree. I'm a very visual person (3D modeller and concept artist by trade!) and I find diagrams and graphs really, really helpful so as many as humanely possible please!

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• Why do we use the Pythagorean theorem in game physics?

  - by Starkers

  I've recently learned that we use Pythagorean theorem a lot in our physics calculations and I'm afraid I don't really get the point. Here's an example from a book to make sure an object doesn't travel faster than a MAXIMUM_VELOCITY constant in the horizontal plane: MAXIMUM_VELOCITY = <any number>; SQUARED_MAXIMUM_VELOCITY = MAXIMUM_VELOCITY * MAXIMUM_VELOCITY; function animate(){ var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; x_velocity = x_velocity / scalar; z_velocity = x_velocity / scalar; } } Let's try this with some numbers: An object is attempting to move 5 units in x and 5 units in z. It should only be able to move 5 units horizontally in total! MAXIMUM_VELOCITY = 5; SQUARED_MAXIMUM_VELOCITY = 5 * 5; SQUARED_MAXIMUM_VELOCITY = 25; function animate(){ var x_velocity = 5; var z_velocity = 5; var squared_horizontal_velocity = (x_velocity * x_velocity) + (z_velocity * z_velocity); var squared_horizontal_velocity = 5 * 5 + 5 * 5; var squared_horizontal_velocity = 25 + 25; var squared_horizontal_velocity = 50; // if( squared_horizontal_velocity <= SQUARED_MAXIMUM_VELOCITY ){ if( 50 <= 25 ){ scalar = squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY; scalar = 50 / 25; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Now this works well, but we can do the same thing without Pythagoras: MAXIMUM_VELOCITY = 5; function animate(){ var x_velocity = 5; var z_velocity = 5; var horizontal_velocity = x_velocity + z_velocity; var horizontal_velocity = 5 + 5; var horizontal_velocity = 10; // if( horizontal_velocity >= MAXIMUM_VELOCITY ){ if( 10 >= 5 ){ scalar = horizontal_velocity / MAXIMUM_VELOCITY; scalar = 10 / 5; scalar = 2.0; x_velocity = x_velocity / scalar; x_velocity = 5 / 2.0; x_velocity = 2.5; z_velocity = z_velocity / scalar; z_velocity = 5 / 2.0; z_velocity = 2.5; // new_horizontal_velocity = x_velocity + z_velocity // new_horizontal_velocity = 2.5 + 2.5 // new_horizontal_velocity = 5 } } Benefits of doing it without Pythagoras: Less lines Within those lines, it's easier to read what's going on ...and it takes less time to compute, as there are less multiplications Seems to me like computers and humans get a better deal without Pythagorean theorem! However, I'm sure I'm wrong as I've seen Pythagoras' theorem in a number of reputable places, so I'd like someone to explain me the benefit of using Pythagorean theorem to a maths newbie. Does this have anything to do with unit vectors? To me a unit vector is when we normalize a vector and turn it into a fraction. We do this by dividing the vector by a larger constant. I'm not sure what constant it is. The total size of the graph? Anyway, because it's a fraction, I take it, a unit vector is basically a graph that can fit inside a 3D grid with the x-axis running from -1 to 1, z-axis running from -1 to 1, and the y-axis running from -1 to 1. That's literally everything I know about unit vectors... not much :P And I fail to see their usefulness. Also, we're not really creating a unit vector in the above examples. Should I be determining the scalar like this: // a mathematical work-around of my own invention. There may be a cleverer way to do this! I've also made up my own terms such as 'divisive_scalar' so don't bother googling var divisive_scalar = (squared_horizontal_velocity / SQUARED_MAXIMUM_VELOCITY); var divisive_scalar = ( 50 / 25 ); var divisive_scalar = 2; var multiplicative_scalar = (divisive_scalar / (2*divisive_scalar)); var multiplicative_scalar = (2 / (2*2)); var multiplicative_scalar = (2 / 4); var multiplicative_scalar = 0.5; x_velocity = x_velocity * multiplicative_scalar x_velocity = 5 * 0.5 x_velocity = 2.5 Again, I can't see why this is better, but it's more "unit-vector-y" because the multiplicative_scalar is a unit_vector? As you can see, I use words such as "unit-vector-y" so I'm really not a maths whiz! Also aware that unit vectors might have nothing to do with Pythagorean theorem so ignore all of this if I'm barking up the wrong tree. I'm a very visual person (3D modeller and concept artist by trade!) and I find diagrams and graphs really, really helpful so as many as humanely possible please!

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• Determining the angle to fire a shot when target and shooter moves, and bullet moves with shooter velocity added in

  - by Azaral

  I saw this question: Predicting enemy position in order to have an object lead its target and followed the link in the answer to stack overflow. In the stack overflow page I used the 2nd answer, the one that is a large mathematical derivation. My situation is a little different though. My first question though is will the answer provided in the stack overflow page even work to begin with, assuming the original circumstances of moving target and stationary shooter. My situation is a little different than that situation. My target moves, the shooter moves, and the bullets from the shooter start off with the velocities in x and y added to the bullets' x and y velocities. If you are sliding to the right, the bullets will remain in front of you as you move so as long as your velocity remains constant. What I'm trying to do is to get the enemy to be able to determine where they need to shoot in order to hit the player. Unless the player and enemy is stationary, the velocity from the ship adding to the velocity of the bullets will cause a miss. I'd rather like to prevent that. I used the formula in the stack overflow answer and did what I thought were the appropriate adjustments. I've been banging at this for the last four hours and I just can't make it click. It is probably something really simple and boneheaded that I am missing (that seems to be a lot of my problems lately). Here is the solution presented from the stack overflow answer: It boils down to solving a quadratic equation of the form: a * sqr(x) + b * x + c == 0 Note that by sqr I mean square, as opposed to square root. Use the following values: a := sqr(target.velocityX) + sqr(target.velocityY) - sqr(projectile_speed) b := 2 * (target.velocityX * (target.startX - cannon.X) + target.velocityY * (target.startY - cannon.Y)) c := sqr(target.startX - cannon.X) + sqr(target.startY - cannon.Y) Now we can look at the discriminant to determine if we have a possible solution. disc := sqr(b) - 4 * a * c If the discriminant is less than 0, forget about hitting your target -- your projectile can never get there in time. Otherwise, look at two candidate solutions: t1 := (-b + sqrt(disc)) / (2 * a) t2 := (-b - sqrt(disc)) / (2 * a) Note that if disc == 0 then t1 and t2 are equal. If there are no other considerations such as intervening obstacles, simply choose the smaller positive value. (Negative t values would require firing backward in time to use!) Substitute the chosen t value back into the target's position equations to get the coordinates of the leading point you should be aiming at: aim.X := t * target.velocityX + target.startX aim.Y := t * target.velocityY + target.startY Here is my code, after being corrected by Sam Hocevar (thank you again for your help!). It still doesn't work. For some reason it never enters the section of code inside the if(disc = 0) (obviously because it is always less than zero but...). However, if I plug the numbers from my game log on the enemy and player positions and velocities it outputs a valid firing solution. I have looked at the code side by side a couple of times now and I can't find any differences. There has got to be something simple I'm missing here. If someone else could look at this code and determine what is going on here I'd appreciate it. I know it's not going through that section because if it were, shouldShoot would become true and the enemy would be blasting away at the player. This section calls the function in question, CalculateShootHeading() if(shouldMove) { UseEngines(); } x += xVelocity; y += yVelocity; CalculateShootHeading(); if(shouldShoot) { ShootWeapons(); } UpdateWeapons(); This is CalculateShootHeading(). This is inside the enemy class so x and y are the enemy's x and y and the same with velocity. One output from my game log gives Player X = 2108, Player Y = -180.956, Player X velocity = 10.9949, Player Y Velocity = -6.26017, Enemy X = 1988.31, Enemy Y = -339.051, Enemy X velocity = 1.81666, Enemy Y velocity = -9.67762, 0 enemy projectiles. The output from the console tester is Bullet position = 2210.49, -239.313 and Player Position = 2210.49, -239.313. This doesn't make any sense. The only thing that could be different is the code or the input into my function in the game and I've checked that and I don't think that it is wrong as it's updated before this and never changed. float const bulletSpeed = 30.f; float const dx = playerX - x; float const dy = playerY - y; float const vx = playerXVelocity - xVelocity; float const vy = playerYVelocity - yVelocity; float const a = vx * vx + vy * vy - bulletSpeed * bulletSpeed; float const b = 2.f * (vx * dx + vy * dy); float const c = dx * dx + dy * dy; float const disc = b * b - 4.f * a * c; shouldShoot = false; if (disc >= 0.f) { float t0 = (-b - std::sqrt(disc)) / (2.f * a); float t1 = (-b + std::sqrt(disc)) / (2.f * a); if (t0 < 0.f || (t1 < t0 && t1 >= 0.f)) { t0 = t1; } if (t0 >= 0.f) { float shootx = vx + dx / t0; float shooty = vy + dy / t0; heading = std::atan2(shooty, shootx) * RAD2DEGREE; } shouldShoot = true; }

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